Question : A can complete a certain work in 35 days and B can complete the same work in 15 days. They worked together for 7 days, and then B left the work. In how many days will A alone complete 60% of the remaining work?
Option 1: 10
Option 2: 15
Option 3: 8
Option 4: 7
Correct Answer: 7
Solution :
Given,
A completes the work in 35 days.
B completes the work in 15 days.
A's 1 day's work $=\frac{1}{35}$
B's 1 day's work $=\frac{1}{15}$
So, (A + B)'s 1 day's work = $\frac{1}{35}+\frac{1}{15}=\frac{7 + 3}{105}=\frac{2}{21}$
⇒ Work completed by A + B in 7 days $=\frac{2}{21} × 7=\frac{2}{3}$
So, Remaining work = $1 - \frac23=\frac13$
⇒ 60% of the remaining work = $\frac{3}{5}×\frac{1}{3}=\frac{1}{5}$
So, time taken by A to finish this work = $\frac{1}{5}× 35= 7$ days
Hence, the correct answer is 7.
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